Abelian rank of normal torsion-free finite index subgroups of polyhedral groups
Copyright policy )Abelian rank of normal torsion-free finite index subgroups of polyhedral groups
Suppose that P P is a convex polyhedron in the hyperbolic 3 3 -space with finite volume and P P has integer ( > 1 ) ( > 1) submultiples of π \pi as dihedral angles. We prove that if the rank of the abelianization of a normal torsion-free finite index subgroup of the polyhedral group G G associated to P P is one, then P P has exactly one ideal vertex of type ( 2 , 2 , 2 , 2 ) (2,2,2,2) and G G has an index two subgroup which does not contain any one of the four standard generators of the stabilizer of the ideal vertex.
Discontinuous groups of transformations, torsion-free finite index subgroup, Other geometric groups, including crystallographic groups, Topology of general \(3\)-manifolds, convex polyhedron in hyperbolic 3-space, Reflection groups, reflection geometries, ideal vertex, polyhedral group
Discontinuous groups of transformations, torsion-free finite index subgroup, Other geometric groups, including crystallographic groups, Topology of general \(3\)-manifolds, convex polyhedron in hyperbolic 3-space, Reflection groups, reflection geometries, ideal vertex, polyhedral group
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